The correct answer is 4/7.

Key Points

• The probability of selecting a green ball is the number of green balls divided by the total number of balls, which is 4/7.
  • There are a total of 7 balls in the bag (3 red + 4 green). 
• The probability of selecting a green ball from a bag containing 3 red balls and 4 green balls is 4/7

Additional Information

• Step 1:
  • Find the total number of balls in the bag:
  • 3 red balls + 4 green balls = 7 balls
• Step 2:
  • Find the number of green balls in the bag:
  • 4 green balls
• Step 3:
  • Find the probability of selecting a green ball by dividing the number of green balls by the total number of balls:
  • 4/7

Therefore, the answer is 4/7.

Important Points

• Probability:
  • the measure of the likelihood of an event occurring, expressed as a number between 0 and 1 
• Conditional probability:
  • the probability of an event occurring given that another event has occurred 
• Independent events:
  • events that the outcome of one does not affect the outcome of the other. 
• Complementary events:
  • events that are mutually exclusive and add up to 1. 
• Sample space:
  • the set of all possible outcomes in a probability experiment. 
• Event:
  • a subset of the sample space. 
• Classical definition of probability:
  • the ratio of the number of favorable outcomes to the number of possible outcomes. 
• Empirical probability:
  • the relative frequency of an event in a large number of trials.

The correct answer is Pink Sandstone.

Key Points

• The sandstone was majorly used for the construction of the main structure of Ayodhya Ram Mandir.
• The use of Steel or Iron has been completely avoided in the construction of Ram Mandir.
• Instead, traditional construction materials have been used in its construction to reflect an alignment with traditional building practices along with an emphasis on sustainability. 
• Major construction materials used in the construction of Ram Mandir are:
  • Bansi Paharpur Pink Sandstone from Rajasthan’s Bharatpur district have been used in the main temple structure.
  • Granite Stones have been used in the plinths
  • White Makrana and Colored Marbles have been used for the inlay work.
  • Teakwood has been used for the construction of the doors of the temple.
• Special Bricks with “Shri Ram” inscribed on them have been used in its construction.
• These bricks, named Ram Shilas, draw a parallel with the stones used in the construction of Ram Setu, thus intertwining modern craftsmanship with ancient symbolism.

Given:

x² - 2px + 8p - 15 = 0

Concept used:

Quadratic equation: ax² + bx + c = 0

D = b² - 4ac = 0 (For equal roots)

Calculation:

Equation: x² - 2px + 8p - 15 = 0

a = 1, b = -2p and c = 8p - 15

According to the question,

D = b² - 4ac = 0 (For equal roots)

⇒ (-2p)² - 4 × 1 × (8p - 15) = 0

⇒ 4p² - 32p + 60 = 0

⇒ p2 - 8p + 15 = 0

⇒ p² - 5p - 3p + 15 = 0

⇒ p(p - 5) - 3(p - 5) = 0

⇒ (p - 5)(p - 3) = 0

∴ p = 3 or 5

Calculation:

Δ_IE = 1 mA 

Δ_IC = 0.995 mA

From equation (1);

Given:

The angle of elevation of the top of a tower at a point on level ground = 45° 

When moved 20 m towards the tower, the angle of elevation becomes 60°.

Concept used:

tanθ = perpendicular/base

Calculation:

Let the height of the tower (AB) be h

In ΔABC,

Given:

The area of ΔABC is 9 sq. cm, and area of ΔDEF is 16 sq. cm

EF = 2.8

Concept used:

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

Calculation:

ΔABC is similar to ΔDEF,

then (area of Δ ABC)/(area of ΔDEF) = (BC/EF)²

⇒ √(9/16) = BC/2.8 

⇒ BC = 2.8 × 3/4 

⇒ BC = 2.1

∴ The length of BC will be 2.1 cm.

• The shortcut key Ctrl + O is used to open the current document in Windows.

Ctrl + S is often used to save changes to a file.

Ctrl + V is used to paste the contents of the clipboard at the current cursor location.

• Ctrl + C is used to copy the currently highlighted text or object.

• A Lissajous figure is a pattern which is displayed on the screen when sinusoidal signals are applied to both horizontal & vertical deflection plates of CRO.
• These are used to measure the frequency of the given signals and phase difference between the signals.
• From the shape of the Lissajous pattern displayed on CRO screen information about relative phases of signals and the frequency ratio of signals can be determined.
• It is not used for precise measurement; it depends on the type of signals.
• If one frequency is an integral multiple (harmonic) of the other, the pattern will be steady. If not, the figure will not be stationary.

Notes:

Common Lissajous pattern observed when two signals with different phase angle is applied to the two plates is as shown:

Piezoelectric materials are materials that can produce electricity due to mechanical stress, such as compression. These materials can also deform when a voltage is applied.

All piezoelectric materials are non-conductive for the piezoelectric effect to occur and work. They can be separated into two groups:

1) Crystals

2) Ceramics

Extra Information:

• The piezoelectric effect is generally carried out in crystal oscillators, crystal filters, production and detection of sound, piezoelectric inkjet printing, generation of high voltages, electronic frequency generation, microbalances, to drive an ultrasonic nozzle, and ultrafine focusing of optical assemblies.
• On the application of a force resulting in the deformation of the crystal, the charges on the crystal will tend to separate such that one end will be positively charged and the other end of the crystal will be negatively charged.
• If the crystals are oriented accordingly, we can cause efficient charge separation which can be tapped by connecting the arrangement through a closed circuit and this will thus cause flow of current through the circuit.